Physical Source Of Randomness Research Articles

Random Number Generators: Principles and Applications

In this paper, we present approaches to generating random numbers, along with potential applications. Rather than trying to provide extensive coverage of several techniques or algorithms that have appeared in the scientific literature, we focus on some representative approaches, presenting their workings and properties in detail. Our goal is to delineate their strengths and weaknesses, as well as their potential application domains, so that the reader can judge what would be the best approach for the application at hand, possibly a combination of the available approaches. For instance, a physical source of randomness can be used for the initial seed; then, suitable preprocessing can enhance its randomness; then, the output of preprocessing can feed different types of generators, e.g., a linear congruential generator, a cryptographically secure one and one based on the combination of one-way hash functions and shared key cryptoalgorithms in various modes of operation. Then, if desired, the outputs of the different generators can be combined, giving the final random sequence. Moreover, we present a set of practical randomness tests that can be applied to the outputs of random number generators in order to assess their randomness characteristics. In order to demonstrate the importance of unpredictable random sequences, we present an application of cryptographically secure generators in domains where unpredictability is one of the major requirements, i.e., eLotteries and cryptographic key generation.

Enhancing Quality and Security of the PLL-TRNG

Field Programmable Gate Arrays (FPGAs) are used more and more frequently to implement cryptographic systems, which need random number generators (RNGs) to be embedded in the same device. The main challenge related to the implementation of a generator running inside FPGAs is that the physical source of randomness, such as jittered clock generator, is implemented in the configurable logic area, i.e. in the close vicinity of noisy running algorithms, which can have significant impact on generated numbers or even serve to attack the generator. A possible approach to prevent such influence is the use of Phase-Lock Loops (PLLs), which are separated from the re-configurable logic area inside the FPGA chip. In this paper, we propose a new architecture of the PLL-based TRNG including a method to avoid correlation in the output through control of timing in the sampling process, as well as new embedded tests based on the enhanced stochastic model. We also propose a workflow to help find the best parameters, such as output bitrate and entropy rate. We show that bitrates of around 400 kb/s or more can be achieved, while guaranteeing min-entropy rates per bit higher than 0.98 as required by the latest security standards.

J3Gen: A PRNG for Low-Cost Passive RFID

Pseudorandom number generation (PRNG) is the main security tool in low-cost passive radio-frequency identification (RFID) technologies, such as EPC Gen2. We present a lightweight PRNG design for low-cost passive RFID tags, named J3Gen. J3Gen is based on a linear feedback shift register (LFSR) configured with multiple feedback polynomials. The polynomials are alternated during the generation of sequences via a physical source of randomness. J3Gen successfully handles the inherent linearity of LFSR based PRNGs and satisfies the statistical requirements imposed by the EPC Gen2 standard. A hardware implementation of J3Gen is presented and evaluated with regard to different design parameters, defining the key-equivalence security and nonlinearity of the design. The results of a SPICE simulation confirm the power-consumption suitability of the proposal.

Symmetrization of single-sided or nonsymmetrical distributions: The way to enhance a generation rate of random bits from a physical source of randomness

An efficient method for enhancement of a random bit generation rate from a physical source of randomness is proposed. It is based on the repeated application of the operation of symmetrization of random data. This procedure allows one to transform asymptotically any nonsymmetrical distribution into a perfectly symmetrical one. As a result, one can extract up to 46 uncorrelated and unbiased bits from each variate, increasing an effective rate up to 46 times with respect to the mean frequency of random events. The method was tested with spontaneous switchings in a bistable vertical cavity laser. A statistical analysis of the generated random bit sequences which passed the standard randomness tests (ENT, NIST Statistical Test Suites, and Diehard) is presented.

Probability distribution of energetic-statistical size effect in quasibrittle fracture

The physical sources of randomness in quasibrittle fracture described by the cohesive crack model are discussed and theoretical arguments for the basic form of the probability distribution are presented. The probability distribution of the size effect on the nominal strength of structures made of heterogeneous quasibrittle materials is derived, under certain simplifying assumptions, from the nonlocal generalization of Weibull theory. Attention is limited to structures of positive geometry failing at the initiation of macroscopic crack growth from a zone of distributed cracking. It is shown that, for small structures, which do not dwarf the fracture process zone (FPZ), the mean size effect is deterministic, agreeing with the energetic size effect theory, which describes the size effect due to stress redistribution and the associated energy release caused by finite size of the FPZ formed before failure. Material randomness governs the statistical distribution of the nominal strength of structure and, for very large structure sizes, also the mean. The large-size and small-size asymptotic properties of size effect are determined, and the reasons for the existence of intermediate asymptotics are pointed out. Asymptotic matching is then used to obtain an approximate closed-form analytical expression for the probability distribution of failure load for any structure size. For large sizes, the probability distribution converges to the Weibull distribution for the weakest link model, and for small sizes, it converges to the Gaussian distribution justified by Daniels' fiber bundle model. Comparisons with experimental data on the size-dependence of the modulus of rupture of concrete and laminates are shown. Monte Carlo simulations with finite elements are the subject of ongoing studies by Pang at Northwestern University to be reported later.